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A non elliptic spectral problem related to the analysis of superconducting micro-strip lines

Anne-Sophie Bonnet-Bendhia, Karim Ramdani (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This paper is devoted to the spectral analysis of a non elliptic operator A , deriving from the study of superconducting micro-strip lines. Once a sufficient condition for the self-adjointness of operator A has been derived, we determine its continuous spectrum. Then, we show that A is unbounded from below and that it has a sequence of negative eigenvalues tending to - . Using the Min-Max principle, a characterization of its positive eigenvalues is given. Thanks to this characterization, some conditions...

A non elliptic spectral problem related to the analysis of superconducting micro-strip lines

Anne-Sophie Bonnet-Bendhia, Karim Ramdani (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper is devoted to the spectral analysis of a non elliptic operator A , deriving from the study of superconducting micro-strip lines. Once a sufficient condition for the self-adjointness of operator A has been derived, we determine its continuous spectrum. Then, we show that A is unbounded from below and that it has a sequence of negative eigenvalues tending to -∞. Using the Min-Max principle, a characterization of its positive eigenvalues is given. Thanks to this characterization, some...

A note on embedding into product spaces

M. A. Sofi (2006)

Czechoslovak Mathematical Journal

Using factorization properties of an operator ideal over a Banach space, it is shown how to embed a locally convex space from the corresponding Grothendieck space ideal into a suitable power of E , thus achieving a unified treatment of several embedding theorems involving certain classes of locally convex spaces.

A note on generalized projections in c₀

Beata Deręgowska, Barbara Lewandowska (2014)

Annales Polonici Mathematici

Let V ⊂ Z be two subspaces of a Banach space X. We define the set of generalized projections by V ( X , Z ) : = P ( X , Z ) : P | V = i d . Now let X = c₀ or l m , Z:= kerf for some f ∈ X* and V : = Z l (n < m). The main goal of this paper is to discuss existence, uniqueness and strong uniqueness of a minimal generalized projection in this case. Also formulas for the relative generalized projection constant and the strong uniqueness constant will be given (cf. J. Blatter and E. W. Cheney [Ann. Mat. Pura Appl. 101 (1974), 215-227] and G. Lewicki...

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